let f(x) be a quadratic polynomial with f(2) = 10 and f(-2) =2 then the coefficient of x in f(x)
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let f(x) be a quadratic polynomial with f(2) = 10 and f(-2) =2 then the coefficient of x in f(x)
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Let the quadratic equation be f(x)=x2+ax+b
Given f(2)=10 and f(−2)=−2
⇒4+2a+b=10 and 4−2a+b=−2
⇒2a+b=6 and 2a−b=6
on solving both equations , we get a=3 and b=0
Therefore, the coefficient of x in f(x) is 3.
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[tex] \bold{Let \: the \: quadratic \: equation \: be \: f(x)=x }[/tex]
[tex] \bold{2 + ax + b}[/tex]
[tex] \bold{Given \: f(2)=10 \: and \: f(−2)=−2}[/tex][tex] \bold{⇒4+2a+b=10 \: and \: 4−2a+b=−2}\\\bold{⇒2a+b=6 \: and \: 2a−b=6}[/tex]
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[tex] \bold{ \: solving \: equations \: , we \: get \: a=3 \: and \: b=0}[/tex]
[tex] \bold{Therefore, the \: coefficient \: of \: x \: in \: f(x) \: is \: 3.}[/tex]